For example, you double-click a line in the Find panel, and the cursor jumps to the main text window -- but the Find panel is still hogging half the screen, and you have to close it manually (or do Ctrl-F12)?

Click the Undockicon of an open panel (top right corner, hover over the icons for the tooltip that says "Undock"). Now, whenever the focus leaves the panel, it will automatically close.

any occurrence of that text in the file, regardless of scope, is highlighted, even text in comment blocks or String literals.

Why? Since highlighted text accumulates until you hit "Esc" to clear all highlighted text from the buffer, IntelliJ uses different colors to distinguish between "highlight this symbol in scope" and "highlight any matching text in file" modes.

Both of these modes will put markers in the right-hand gutter to to show you at a glance wherever these occurrences may be.